The Thermodynamical Behaviors of Kerr–Newman AdS Black Holes

We reconsider the study of critical behaviors of Kerr–Newman Anti-de Sitter (AdS) black holes in four dimensions. The study is made in terms of the moduli space parameterized by the charge Q and the rotation parameter a, relating the mass M of the black hole and its angular momentum J via the relation a =J/M. Specifically, we discuss such thermodynamical behaviors in the presence of a positive cosmological constant considered as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume. The equation of state for a charged Reissner–Nordstrom AdS black hole predicts a critical universal number depending on the (Q,a) moduli space. In the vanishing limit of the a parameter, this prediction recovers the usual universal number in four dimensions. Then, we find the bounded region of the moduli space allowing the consistency of the model with real thermodynamical variables.